Doping dependence of magnetic excitations of 1D cuprates as probed by Resonant Inelastic x-ray Scattering

TL;DR

This study investigates how magnetic excitations in 1D cuprates evolve with doping using resonant inelastic x-ray scattering, revealing persistent short-range antiferromagnetic correlations despite doping.

Contribution

It provides detailed numerical analysis of magnetic response functions in doped 1D cuprates, highlighting the robustness of magnetic correlations up to 1/8 doping.

Findings

Four-spin response vanishes at π in undoped systems.

Spectral weight shifts to higher energy with doping.

Magnetic correlations remain strong despite doping.

Abstract

We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $\pi$, whereas the two-spin correlator is peaked around $\pi/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\pi$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.